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Set theory, as was quickly recognized by David Hilbert more than 100 years ago, plays a fundamental foundational role in the intellectual underpinning of pure mathematics. Cantor's work on cardinality and well orderings was seen to establish several basic areas of research whose threads we discern today and indeed will be emphasized in this meeting: on the arithmetic of cardinal numbers themselves, and on the descriptive set theory that seeks to analyse the logical complexity of sets definable within mathematical language. Cantor's work derived from his study of trigonometric series, and modern set theory goes back to classical analysis as well as forward to modern Banach space theory, abstract algebra, ergodic theory, and dynamical systems to find fruitful applications.